Envelope-based amplitude mapping for cochlear implant stimulus

ABSTRACT

An envelope based amplitude mapping achieves the signal compression required to provide a natural sound level without the high processor loading or waveform alteration. In a preferred embodiment, the output of a family of parallel bandpass filters is processed by an envelope detector, followed by decimation. The resulting reduced data rate envelope is log mapped to produce a scaling factor for the original high data rate bandpass filter output sequence. The resulting scaled signal determines the current level for stimulation of the cochlea for each frequency band, which stimulation achieves a log mapping of the sound amplitude effect similar to natural hearing, while reducing processor load, and preserving waveform shape.

The present application is a Divisional of U.S. application Ser. No.09/866,096, filed May 25, 2001, now issued as U.S. Pat. No. 6,728,578;which claims the benefit of U.S. Provisional Application Ser. No.60/208,627, filed Jun. 1, 2000, which applications and patent areincorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to cochlear prosthesis used toelectrically stimulate the auditory nerve, and more particularly to aprocess for mapping a signal level into a stimulation current level.

Hearing loss, which may be due to many different causes, is generally oftwo types: conductive and sensorineural. Of these, conductive hearingloss occurs where the normal mechanical pathways for sound to reach thehair cells in the cochlea are impeded, for example, by damage to theossicles. Conductive hearing loss may often be helped by use ofconventional hearing aids, which amplify sound so that acousticinformation does reach the cochlea and the hair cells. Some types ofconductive hearing loss are also amenable to alleviation by surgicalprocedures.

In many people who are profoundly deaf, however, the reason for theirdeafness is sensorineural hearing loss. This type of hearing loss is dueto the absence or the destruction of the hair cells in the cochlea whichare needed to transduce acoustic signals into auditory nerve impulses.These people are unable to derive any benefit from conventional hearingaid systems, no matter how loud the acoustic stimulus is made, becausetheir mechanisms for transducing sound energy into auditory nerveimpulses have been damaged. Thus, in the absence of properly functioninghair cells, there is no way auditory nerve impulses can be generateddirectly from sounds.

To overcome sensorineural deafness, numerous implantable cochlearstimulation systems—or cochlear prosthesis—have been developed whichseek to bypass the hair cells in the cochlear (the hair cells arelocated in the vicinity of the radially outer wall of the cochlea) bypresenting electrical stimulation to the auditory nerve fibers directly,leading to the perception of sound in the brain and an at least partialrestoration of hearing function. The common denominators in most ofthese cochlear prosthesis systems have been the implantation, into thecochlea, of electrodes, and a suitable external source of an electricalsignal for the electrodes.

A cochlear prosthesis operates by direct electrical stimulation of theauditory nerve cells, bypassing the defective cochlear hair cells thatnormally transduce acoustic energy into electrical activity in suchnerve cells. In order to effectively stimulate the nerve cells, theelectronic circuitry and the electrode array of the cochlear prosthesisperform the function of separating the acoustic signal into a number ofparallel channels of information, each representing the intensity of anarrow band of frequencies within the acoustic spectrum. Ideally, theelectrode array would convey each channel of information selectively tothe subset of auditory nerve cells that normally transmitted informationabout that frequency band to the brain. Those nerve cells are arrangedin an orderly tonotopic sequence, from high frequencies at the basal endof the cochlear spiral to progressively lower frequencies towards theapex, and ideally the entire length of the cochlea would be stimulatedto provide a full frequency range of hearing. In practice, this ideal isnot achieved, because of the anatomy of the cochlea which decreases indiameter from the base to the apex, and exhibits variations betweenpatients. Because of these difficulties, known electrodes can only bepromoted to the second turn of the cochlea at best.

The signal provided to the electrode array is generated by a signalprocessing component of the Implantable Cochlear Stimulation (ICS)system. In known ICS systems, the acoustic signal is first processed bya family of parallel bandpass filters. Next the output of each bandpassfilter is independently amplitude mapped into a simulation level using amapping consistent with normal perception. In known systems, the mappingis a compressive mapping that is based on the log of the magnitude ofeach independent sample of the outputs of the band pass filters. The logis taken of the magnitude of each sample, then multiplied by a firstscalar and added to a second scalar, and the sign of each sample is thenapplied to the compressed value. Disadvantageously, the log function canresult in a DC component in the resulting signal, distorts sinusoidalinputs, and is computationally intensive.

The DC component arises from the asymmetry of the input waveform. Thesignal is processed before the amplitude mapping to remove DC bias, andas a result the total area under the waveform, at the output of thebandpass filters, sums to zero. But, the compressive nature of the logfunction reduces narrow high peaks much more than wide low peaks, andthereby creates a DC bias. A wideband speech signal is very asymmetricby nature, so the likelihood of generating such a DC bias is high. Thepresence of the DC bias poses a potential for tissue damage after longterm use, and may cause the charge in a capacitor typically, used forenergy storage in the implantable stimulation circuit, to grow largeresulting in undesirable nonlinear behavior.

The shape of a waveform processed by the amplitude mapping may bedistorted by the compression. For example, samples from the peak of asinusoidal waveform are compressed more than samples between the peaks,and as a result the sinusoid becomes more like a square wave withrounded corners than like a sinusoid. When patients are tested forpsychophysical thresholds, sine waves are used as the stimulatingsignals for each electrode. The frequency of each sine wave is selectedas the center frequency of the band pass filter that processes thesignal for the corresponding electrode in normal system operation. Whenthe threshold levels determined during psychophysical testing are laterapplied to a compressed sinusoid, which compressed sinusoid has the samepeak stimulating current as the original sinusoid that the thresholdsare based on, the perceived loudness may not be the same as with theoriginal sinusoid. Although the peak stimulation currents of theoriginal sinusoid and the compressed sinusoid are the same, theamplitude mapping brings up the “shoulders” on the compressed sinusoid,making it more like a square wave with rounded corners. As a result of“raising the shoulders” of the sinusoid, charge per phase raises, whichresults in the perceived loudness increasing. This increase in perceivedloudness may be significant for patients with a narrow dynamic hearingrange.

The processing required to compute the log of each sample, in eachfrequency band, at a high data rate, is a computationally demandingprocess that expends significant power in the signal processor. Thedevelopment of Behind-The-Ear (BTE) speech processor, and fullyimplantable cochlear stimulators, requires that power consumption bereduced to a minimum. A BTE ICS system is described in U.S. Pat. No.5,824,022 issued Oct. 20, 1998 for ‘Cochlear stimulation systememploying behind-the-ear speech processor with remote control.’Behind-the-ear speech processors offer several advantages, but theirsmall size limits the size of the battery they may carry (which in turnlimits the capacity of the battery.) The small battery size results in arequirement for very low power consumption. Processing, such as thatrequired by known amplitude mapping methods, work against the need toreduce power dissipation. The '022 patent is herein incorporated byreference.

An improvement to the current compressive processing is needed to bothimprove performance, and to reduce the power consumption required forsignal processing.

SUMMARY OF THE INVENTION

The present invention addresses the above and other needs by replacingthe known sample by sample amplitude mapping process in ImplantableCochlear Stimulation (ICS) systems with an envelope based amplitudemapping process. The envelope based amplitude mapping processes operatein parallel on the filtered signals output from parallel bandpassfilters. The filtered signal is first processed by an envelope detector.The result of envelope detection is decimated, and the resultingdecimated envelope is transformed using a compressive function, whichcompressive function is the product of a log mapping of the decimatedenvelope and a reciprocal of the decimated envelope. The transformedsignal is then used to scale the original filtered signal to obtain thestimulation current level for the implanted cochlear electrode array.

In accordance with one aspect of the invention, there is provided anenvelope detector. In a preferred embodiment, the envelope detector is afull wave rectifier followed by a lowpass filter. The lowpass filtercutoff frequency is chosen so as to block the high frequencyfluctuations of individual samples of the audio component of therectified signal, but pass the local averaged value of the signal. Thepreferred cutoff frequency is around 100 Hz, which cutoff determines thelowpass filter design.

It is a further feature of the invention to decimate the signal envelopeto reduce the number of samples processed by the log mapping. The logfunction is computationally intensive, and places a heavy load on thespeech processor. Such high processing loads result in increased powerconsumption. By reducing the number of samples that the log functionoperates on, the overall loading of the speech processor is similarlyreduced, thus reducing power consumption. In a preferred embodiment ofthe invention the decimation factor is 1:16. Such power savings are veryimportant to both Behind-The-Ear ICS systems, and to fully implantableICS systems.

It is an additional feature of the present invention to provide ascaling of the bandpass filter outputs based on a transform which is afunction of the log of the decimated envelope. This approachadvantageously retains the shape of the waveform because the scaling isbased on a measure of the smoothed signal level in the locality of thesample to be scaled, instead of being a function of a single sample, asin known speech processors.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the presentinvention will be more apparent from the following more particulardescription thereof, presented in conjunction with the followingdrawings wherein:

FIG. 1 shows the major elements of a known Implantable CochlearStimulation (ICS) system;

FIG. 2 depicts a functional flow for a prior-art amplitude mapping;

FIG. 3 depicts a functional flow for envelope based amplitude mapping.

FIG. 4 depicts a flow chart for a CIS amplitude mapping application ofthe invention; and

FIG. 5 depicts one embodiment of a flow chart for a CIS amplitudemapping application.

Corresponding reference characters indicate corresponding componentsthroughout the several views of the drawings.

DETAILED DESCRIPTION OF THE INVENTION

The following description is of the best mode presently contemplated forcarrying out the invention. This description is not to be taken in alimiting sense, but is made merely for the purpose of describing thegeneral principles of the invention. The scope of the invention shouldbe determined with reference to the claims.

A functional diagram of a typical Implantable Cochlear Stimulation (ICS)system is shown in FIG. 1. The ICS includes a speech processor 10 thatcould be a wearable speech processor, or a Behind-The-Ear (BTE) speechprocessor. A microphone 12 may be connected to the speech processor 10by a first wire 14, or may be attached to the speech processor 10 as inthe case of a BTE speech processor. The microphone 12 converts acousticenergy into an electrical signal for subsequent processing. The speechprocessor 10 contains a signal processor 16 that processes theelectrical signal from the microphone 12. The output signal of thesignal processor 16 is carried by a second wire 18 to a headpiece 20carried on the patient's head. A first coil 22 transmits the controlsignal 23 from the headpiece 20 to the implantable electronics 24, whichimplantable electronics 24 includes a second coil 26 for receiving thecontrol signal. The implantable electronics 24 processes the controlsignal 23 to generate stimulation current for the electrode array 28,which electrode array 28 is implanted in the patient's cochlea.

The architecture of an ICS system may vary. The ICS may include awearable speech processor that is worn on the users belt and isconnected to a microphone and headpiece by wiring, or a Behind-The-Ear(BTE) speech processor resembling a typical hearing aid, that is wornbehind the patient's ear and retained by an earhook. Another example isa fully implantable ICS in which a speech processor 10 is integratedinto the implantable electronics 26. Those skilled in the are willrecognize that all of these variations require a microphone (or moregenerally a transducer), and a signal processor, to provide astimulation level. All of these variations benefit from the presentinvention as described below.

The human ear adjusts sound intensity with a logarithmic like scaling.Thus, if a sound is 10 times stronger, it may only be perceived to betwice as loud. ICS systems must perform a similar scaling, or mapping,if the patient is to perceive sounds with a natural intensity.Additionally, such logarithmic scaling has the advantage of providingintelligible hearing for low level sounds, without overwhelming thepatient when loud sounds are encountered.

A functional flow for a single channel of prior-art amplitude mapping isshown in FIG. 2. In known systems, there may be from 4 to 30 suchparallel channels operating in different frequency bands. The microphone12 provides an electrical signals to a bandpass filters 32. The bandpassfilter 32 process the electrical signal 30 to generate a filtered signal34. The filtered signal 34 is then processed by a mapper 36 whichoutputs the mapped signal 38. The mapper 36 maps the electrical signal30 level measured by the microphone 12 into an electrical stimulationlevel to be provided to the electrode array 28. In a preferredembodiment the mapper 36 is a log mapper, reflecting normal humanhearing. Those skilled in the are will recognize that other mapping mayproduce similar results and those other mappings are withing the scopeof the present invention. The mapped signal 38 is processed by outputprocessing 40 which outputs the stimulation signal 42 which is providedto the electrode array 28. The log mapper 36 operates on every signalprocessed by the amplitude mapping.

A first embodiment of the present invention, depicted by one channel ofan envelope based amplitude mapping applied to Simultaneous AnalogStimulation (SAS), is shown in FIG. 3. In practice, there are from 4 to30 such parallel channels operating in different frequency bands. Theprocessing up to and including the bandpass filter 32 is unchanged fromknown systems. The sample rate for the filtered signal 34 is between 10KHz and 25 KHz and is preferably 13 KHz or 17 KHz. Identical filteredsignals 34 produced by the bandpass filter 32 are carried on two paths.The top paths in FIG. 3 represents the heart of the envelope basedamplitude mapping. An envelope detector 44 computes an envelop signal 46from the filtered signal 34. In a preferred embodiment the envelopedetector 44 is a full wave rectifier followed by a lowpass filter with acutoff of 100 Hz. The particular envelope detector 44 that is best for aspecific ICS system depends on the details of processing that precedesthe envelope detector 44. Various other implementations of envelopedetectors will be apparent to those skilled in the art, and thesevariations are intended to fall within the scope of the presentinvention.

The next step in the processing shown in FIG. 3 is a decimator 48. Thedecimator 48 creates a decimated signal 50 by reducing the sample rateby only passing every M^(th) value of the envelope signal 46. The samplerate of the decimated signal 50 may be between 50 Hz and 1000 Hz and is800 Hz in a preferred embodiment. The decimated sample rate in otherembodiments of the invention may vary based on other parameters of ICSthe present invention is exercised in, and on the preferences of thepatient. While the envelope detector and decimator are shown as separateprocessing steps, in a preferred implementation, the lowpass filter anddecimator are combined into a single Finite Impulse Response (FIR)filter.

Continuing on in FIG. 3, a log mapper 52 computes a mapped signal 54from the decimated signal 50 by taking a compressive transformation ofthe decimated signal 50. The preferred transformation is of the formF′(x)=F(x)/x, where F(x)=C1*log(x)+C2. The division by x is required dueto the multiplying step described below. C1 and C2 are based onpsycho-acoustical phenomena and are patient dependent. Specifically,during a fitting process, measurements are made for each patient, and C1and C2 are determined for the individual patient based on thosemeasurements.

The mapped signal 54 may be viewed as a scaling factor related to theaverage level of the filtered signal 34 in the locality of the samplethe scaling is applied to. A multiplier 56, multiplies the mapped signal54 times the original filtered signal 34, to generate an envelope basedamplitude mapping output signal 58. The mapped signal 54 sample rate(hereafter the second sample rate) is lower than the filtered signal 34sample rate (hereafter the first sample rate.) If the first sample rateis not substantially higher than the second sample rate, for example,the first sample rate is less than sixteen times the second sample rate,the mapped signal 54 may be used directly by the multiplier 56. If thefirst sample rate is substantially higher than the second sample rate,for example, the first sample rate is more than sixteen times the secondsample rate, the mapped signal 54 may be linearly interpolated to thefirst sample rate.

The envelope based amplitude mapping described above for SAS amplitudemapping may also be applied to Continuous Interleaved Sampler (CIS)amplitude mapping. A flow chart for a CIS amplitude mappingincorporating the present invention is shown in FIG. 4. The microphone12 and bandpass filter 32 are the same as in FIGS. 2 and 3. The filteredsignal 34 is processed by a second envelope detector 60 to produce asecond envelope signal 62, and the envelope signal 62 is processed by asecond decimator 64, to generate a second decimated signal 66. Apreferred envelope detector 60 comprises a full wave rectifier and a lowpass filter. The lowpass filter has a cut off frequency of about 800 Hzto 2000 Hz, preferably 800 Hz. While the envelope detector and decimatorare shown as separate processing steps, in a preferred implementation,the lowpass filter and decimator are combined into a single FiniteImpulse Response (FIR) filter.

Continuing with FIG. 4, the decimated signal 66 is processed by a thirdenvelope detector 68 to obtain a third envelope signal 70, and theenvelope signal 70 is processed by a third decimator 72 to obtain athird decimated signal 74. A preferred envelope detector 68 comprises afull wave rectifier and a low pass filter. The lowpass filter has a cutoff frequency of about 40 Hz to 100 Hz, preferably 40 Hz. While theenvelope detector and decimator are shown as separate processing steps,in a preferred implementation, the lowpass filter and decimator arecombined into a single Finite Impulse Response (FIR) filter.

The decimated signal 74 is processed by the log mapper 52 to generate asecond mapped signal 78. The mapped signal 78 and the decimated signal66 are provided to the multiplier 80, resulting in the second outputsignal 82, which output signal 82 is provided to a pulse generator. Oneoutput signal 82 is provided for each pulse in CIS processing. Thedecimated signal 66 is at a higher data rate than the mapped signal 78.In a preferred embodiment, the mapped signal 78 is interpolated to thedata rate of the decimated signal 66 in the multiplier 80.

A third embodiment comprising a second application of the presentinvention to CIS amplitude mapping is shown in FIG. 5. The microphone 12and bandpass filter 32 are the same as in FIGS. 2, 3, and 4. Thefiltered signal 34 is processed by two parallel paths in the second CISembodiment. A fourth envelope detector 84 to produce a fourth envelopesignal 86, and the envelope signal 86 is processed by a fourth decimator88, to generate a fourth decimated signal 90. A preferred envelopedetector 84 comprises a half wave rectifier and a low pass filter. Thelowpass filter has a cut off frequency of about 800 Hz to 2000 Hz,preferably 800 Hz. While the envelope detector and decimator are shownas separate processing steps, in a preferred implementation, the lowpassfilter and decimator are combined into a single Finite Impulse Response(FIR) filter.

Continuing with FIG. 5, the filtered signal 34 is processed by a fifthenvelope detector 92 to obtain a fifth envelope signal 94, and theenvelope signal 94 is processed by a fifth decimator 96 to obtain afifth decimated signal 98. A preferred envelope detector 92 comprises afull wave rectifier and a low pass filter. The lowpass filter has a cutoff frequency of about 40 Hz to 100 Hz, preferably 40 Hz. While theenvelope detector and decimator are shown as separate processing steps,in a preferred implementation, the lowpass filter and decimator arecombined into a single Finite Impulse Response (FIR) filter.

The decimated signal 98 is processed by the log mapper 52 to generate athird mapped signal 102. The mapped signal 102 and the decimated signal90 are provided to the multiplier 80, resulting in a third output signal104, which output signal 104 is provided to a pulse generator. Oneoutput signal 104 is provided for each pulse in CIS processing. Thedecimated signal 90 is at a higher data rate than the mapped signal 102.In a preferred embodiment, the mapped signal 102 is interpolated to thedata rate of the decimated signal 90 in the multiplier 80.

The log mapping function is used to compress the stimulation current ina manner similar to the natural compression of the human ear. Thoseskilled in the art will recognize that other compressive mappingfunctions produce similar results, and fall within the scope of thepresent invention. Similarly, the embodiment described above includes afamily of parallel band pass filters, but the use of a Fast FourierTransformation (FFT) would produce similar results and is within thescope of the invention.

Thus an envelope amplitude mapping for cochlear stimulation has beenpresented to both reduced computational requirements, and improvesperformance. In applications requiring miniature devices, suchreductions in computational requirements meet the important goal ofextending battery life. Further, the improved performance provides moreaccurate hearing and thus represents a step forward in restoring naturalsounding hearing to the deaf.

While the invention herein disclosed has been described by means ofspecific embodiments and applications thereof, numerous modificationsand variations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

1. An Implantable Cochlear Stimulation (ICS) system including: amicrophone a speech processor; and an electrode array; wherein thespeech processor includes at least one filter and at least onecompressive mapping, wherein the microphone converts acoustic energyinto an electrical signal, and wherein the at least one filter processesthe electrical signal to generate at least one filtered signal andwherein the compressive mapping includes means for converting the atleast one filtered signal into at least one output signal maintaininglow frequency information of the at least one output signal, wherein thecompressive mapping is performed at a reduced rate.
 2. An ImplantableCochlear Stimulation (ICS) system including: a microphone; a speechprocessor; and an electrode array; wherein the speech processor includesat least one filter and at least one compressive mapping, wherein themicrophone converts acoustic energy into an electrical signal, andwherein the at least one filter processes the electrical signal togenerate at least one filtered signal and wherein the compressivemapping includes means for converting the at least one filtered signalinto at least one output signal, wherein the compressive mapping isperformed at a reduced rate; wherein the at least one filter is at leastone bandpass filter, and the compressive mapping comprises envelopebased compressive mapping includes at least one envelope detector, atleast one decimator, at least one compressive mapper, and at least onemultiplier; wherein the at least one envelope detector converts the atleast one filtered signal into at least one envelope signal, and whereinthe at least one decimator converts the at least one envelope signalinto at least one decimated signal, wherein the at least one decimatedsignal is at a lower data rate than the at least one envelope signal,and wherein the compressive mapper converts the at least one decimatedsignal into at least one mapped signal, and wherein the multipliermultiplies the at least one mapped signal times the at least oneelectrical signal to generate the at least one output signal.
 3. AnImplantable Cochlear Stimulation (ICS) system including: a microphone; aspeech processor; and an electrode array; wherein the speech processorincludes at least one filter and at least one compressive mapping,wherein the microphone converts acoustic energy into an electricalsignal, and wherein the at least one filter processes the electricalsignal to generate at least one filtered signal and wherein thecompressive mapping includes means for converting the at least onefiltered signal into at least one output signal, wherein the compressivemapping is performed at a reduced rate; wherein the at least one filteris at least one bandpass filter, and the compressive mapping comprises asecond bin averager, a third bin averager, a log mapper, and amultiplier; wherein the second bin averager averages the filtered signalto generate a second averaged signal, the third bin averager averagesthe second averaged signal to generate a third averaged signal, the logmapper compressively maps the third averages signal to generate a mappedsignal, and the multiplier multiplies the mapped signal times the secondaveraged signal to generate the output signal.
 4. The system of claim 3wherein: the second averaged signal is at a data rate of about 800 Hz;the third averaged signal and the mapped signal at a data rate of about100 Hz; and the output signal is provided to a pulse generator.
 5. AnImplantable Cochlear Stimulation (ICS) system including envelope basedamplitude mapping, comprising: an implantable part including anelectrode array; and a speech processor including a microphone and asignal processor, wherein the microphone converts acoustic energy intoan electrical signal provided to the signal processor, and wherein thesignal processor includes: means for filtering the electrical signal togenerate at least one filtered signal; means for computing at least oneenvelope signal from the at least one filtered signal maintaining lowfrequency information of the at least one envelope signal; means forcomputing at least one decimated signal from the at least one signalenvelope; means for computing at least one mapped signal from the atleast one decimated signal; and means for computing at least one outputsignal from the at least one mapped signal and the at least one filteredsignal.
 6. The system of claim 1 wherein the means for filtering theelectrical signal comprising a family of at least one parallel band passfilter.
 7. The system of claim 1 wherein the means for computing atleast one envelope signal comprises a full wave rectifier followed by alowpass filter.
 8. An Implantable Cochlear Stimulation (ICS) systemincluding envelope based amplitude mapping, comprising: an implantablepart including an electrode array; and a speech processor including amicrophone and a signal processor, wherein the microphone convertsacoustic energy into an electrical signal provided to the signalprocessor, and wherein the signal processor includes means for filteringthe electrical signal to generate at least one filtered signal, meansfor computing at least one envelope signal from the at least onefiltered signal, means for computing at least one decimated signal fromthe at least one signal envelope, means for computing at least onemapped signal from the at least one decimated signal, and means forcomputing at least one output signal from the at least one mapped signaland the at least one filtered signal; wherein the means for computing atleast one output signal multiplies the at least one mapped signal timesthe electrical signal to generate an output signal for the electrodearray.
 9. An Implantable Cochlear Stimulation (ICS) system includingenvelope based amplitude mapping, comprising: an implantable partincluding an electrode array; and a speech processor including amicrophone and a signal processor, wherein the microphone convertsacoustic energy into an electrical signal provided to the signalprocessor, and wherein the signal processor includes means for filteringthe electrical signal to generate at least one filtered signal, meansfor computing at least one envelope signal from the at least onefiltered signal, means for computing at least one decimated signal fromthe at least one signal envelope, means for computing at least onemapped signal from the at least one decimated signal, and means forcomputing at least one output signal from the at least one mapped signaland the at least one filtered signal; wherein the means for computingthe at least one mapped signal comprises a mapping function F′(x),wherein F′(x) is F(x)/x, and wherein x is the decimated signal, andwherein F(x) is the desired mapping between the at least one filteredsignal and the at least one output signal.
 10. The system of claim 9wherein F(x) is a compressive mapping of x.
 11. The system of claim 10wherein the compressive mapping of x is a log mapping.